Algebra 1 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities



SOL Review Materials
The student will graph linear equations and linear inequalities in two variables, including
a)   determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined.
Essential Knowledge and Skills 
  • Find the slope of the line, given the equation of a linear function.
  • Find the slope of a line, given the coordinates of two points on the line.
  • Find the slope of a line, given the graph of a line.
  • Recognize and describe a line with a slope that is positive, negative, zero, or undefined.
Essential Understandings
  • Changes in slope may be described by dilations or reflections or both.
  • The slope of a line represents a constant rate of change in the dependent variable when the independent variable changes by a  constant amount.
  • The product of the slopes of perpendicular lines is -1 unless one of the lines has an undefined slope.
Vertical Articulation
  1. SOL 7.15 - a) solve one-step inequalities; b) graph solutions on number line
  2. SOL 8.15 - b) solve two-step linear inequalities and graph results on number line; c) identify properties of operations used to solve
  3. SOL 8.16 - graph linear equations in two variables
  4. SOL AFDA.2 - use transformations to write equations, given graph of function (linear/quad/exponential/log)
  5. SOL AII.6 - recognize general shape of function (absolute value/square root/cube root/rational/poly/exponential/ log) families/ convert between graphic and symbolic forms of functions ‐ transformational approach to graphing
Instructional Materials
  1. VDOE ESS Lesson: Slope-2-Slope - Equations and Inequalities (PDF) - Investigating slope of horizontal and vertical lines and graphing a line (Word)
  2. VDOE ESS Lesson: Slippery Slope - Equations and Inequalities (PDF) - Writing equations of lines (Word)
  3. VDOE ESS Lesson: The Submarine - Equations and Inequalities (PDF) - Investigating slope as rate of change (Word)
  4. VDOE ESS Lesson: Equations of Lines - Equations and Inequalities (PDF) - Writing equations of lines (Word)
  5. Notes: Graphing and Transforming Linear Equations (doc) | Answer Key (pdf)
Real World Lessons
  1. Den Meyer: Joulies - Do you think Joulies will work as advertised?
  2. Mathalicious: Can Music Kill You? - Is there a relationship between music tempo and heart rate?
  3. Mathalicious: Datelines - Is the "half plus seven" rule for May-December relationships a good one?
  4. Mathalicious: Domino Effect - How much is Domino's really charging you for pizza…and toppings?
  5. Mathalicious: Donut Stand - What does a little donut stand in Virginia have to do with rates of change, limits, average and marginal cost?
  1. VDOE ESS: Silent Bingo Game (pdf)
  2. VDOE ESS: Slope-2-Slope Puzzle (pdf) | Answer Key (pdf)
  3. VDOE ESS: Slope-Intercept Cards (pdf)
  4. Worksheet: Graphing and Transforming Linear Equations CW (doc)
  5. Worksheet: Graphing and Transforming Linear Equations HW (doc)
  1. SOL Mini Quiz
  1. Mathematics Assessment Project: A17:Linear Graphs - Apprentice - In this task, you are asked to match equations with linear graphs.
  2. JMU Pivotal Question: Determine Ordered Pairs Given Slope (doc)
  3. JMU PIvotal Question: Graphing - Is Claire Correct? (doc)
  4. JMU Pivotal Question: Parallel Lines (doc)
  1. Video: PH Graphing an equation Using Slope-Intercept Form
  2. Video: PH Graphing Using Point-Slope Form
Explore Learning
  1. Distance-Time and Velocity-Time Graphs - Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.
  2. Function Machines 2 (Functions, Tables, and Graphs) - Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph.
  3. Modeling Linear Systems - Activity A - Experiment with a system of two lines representing a cat‑and‑mouse chase.  Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real‑world meaning to slope, y‑intercept, and the intersection of lines.
  4. Slope - Activity B - Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes.
  1. Interactive Notes: Graphing Linear Equations - lessons and practice problems at
  2. Notes: Graphing Using Slope and Y-intercept - notes on graphing using slope and y-intercept at
  3. Notes: Writing Equations of Lines - notes on finding the slope at
  4. Interactive Notes: Writing Equations of Lines - lessons and practice problems at
  5. Interactive: Slope Slider - manipulate a linear function in the form of f(x) = mx + b at
  6. Interactive: Exploring Slope-Intercept Form - mathlet from GeoGebra
  7. Interactive: Investigating Horizontal Lines - mathlet from GeoGebra
  8. Interactive: Investigating Vertical Lines - mathlet from GeoGebra
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Common Core Standards